48 ILLINOIS BIOLOGICAL MONOGRAPHS ^ [168 



1916, pp. 842-844), Driesch (1909), and Sir Oliver Lodge (1913) suggest 

 that there is an organized force, entelechy, or vital force and that so 

 long as the cell is ahve this force regulates the metabolism but as soon as this 

 force is destroyed or inhibited the metabolic processes cease, i.e., the machinery 

 no longer works and the cell dies. Robertson (1908) suggests that the normal 

 rate of growth is an autocatalytic process. And finally Troland (1917) defends 

 the thesis that all biological enigmas as he calls them are explainable on the 

 basis of enzymes either autocatalytic or heterocatalytic. Thus it appears 

 from either the mechanistic or the vitaUstic view and experimental data that 

 metaboUsm can be conceived of as a self-perpetuating mechanism and that 

 when metabolism is interfered with beyond a certain Umit, this mechanism 

 or metabolism is progressively depressed or inhibited. That is, metabolism 

 continues within a certain hmit at a normal rate; enzymes, excitors, or anti- 

 bodies inhibiting autolysis are Uberated or generated which stimulate meta- 

 boUsm or allow metabolic activities to continue at a normal rate. But as 

 rapidly as the rate of metabolism is reduced below this normal rate, beyond 

 a certain limit, the rate of Hberating or generating enzymes or antibodies 

 is reduced in proportion to the reduction of the rate of Hberation or generation 

 of the cell enzymes or antibodies. In other words, we are dealing here with 

 the rate of inhibition of a process, metabolism, the rate of which is uniform 

 imder any fixed set of normal conditions. One of the factors of a normal con- 

 dition is a normal rate of metabolism. Thus when the rate of metabolism is 

 reduced below the normal the conditions become abnormal. This in turn 

 becomes an inhibiting factor which increases progressively with the decrease 

 in the rate of metabolism, i.e., it becomes self -inhibiting. This portion of 

 the effect on the speed of inhibition of metaboHsm is thus proportional to the 

 product of the amount of reduction in the rate of metabolism at any time t, 

 and the reduced rate of metaboUsm at that time. This can be compared 

 in the speed of the reduction of the rate of metaboUsm to the velocity 

 of an autocatalytic reaction and can thus be expressed mathematicaUy 



dz 



— = K2z(M-z). That is, at any given time, /, the speed of inhibition of meta- 

 dt 



boUsm is in proportion to the product of the reduced rate of metaboUsm and the 

 rate of metaboUsm at the given time. M= normal rate of metaboUsm under 

 any fixed set of conditions, z= amount of reduction of rate of metaboUsm at 

 any given time, K2=a constant representing the efficiency of the reduced 

 rate of metaboUsm in inhibiting metaboUc processes, i.e., in inhibiting the 

 activation or action of the metaboUc enzymes or antibodies or representing 

 the liberation of autolytic enzymes, and /= time. The amount of reduction 

 z in the rate of metaboUsm after any time t is due not only to the auto- 

 inhibitory process but also to the continuous action of the protoplasmic 

 poison introduced. But the equation above takes into consideration only 

 the reduction due to the autoinhibitory process, and does not take into 



